Problem: For a list of five positive integers, none greater than 100, the mean is 1.5 times the mode. If 31, 58, 98, $x$ and $x$ are the five integers, what is the value of $x$?
The mean of the list 31, 58, 98, $x$ and $x$ is $(31+58+98+2x)/5=(187+2x)/5$, and the mode is $x$.  Solving $1.5x=(187+2x)/5$ we find $x=\boxed{34}$.